On previous pages, I arranged the number
series in various graphical ways to highlight the prime number distributions.
These included rectangular and triangular arrays.
Here is an another way of arranging the numbers, in a hexagonal arrangement
made up of close-packed circles:
Starting from the center, you can see that I numbered each
circle with consecutive whole numbers, sequentially going around the center
circle. When each "number ring" around the center is filled, the circle
immediately above the last one takes up the count. The circles that
contain a prime number are painted black.
I ginned up a VisualBasictm program to explore the
resulting prime patterns on a larger scale. In this program, I let each
ring of numbers be a circle around the origin, rather than showing the flat
sides of hexagons. (The mathematical section of my brain -- the size of
a small Spanish peanut -- found it too hard to flatten the sides while keeping
the number sequence correctly ordered.) I painted the circles containing
prime numbers white in this array:
Here is a larger array of the same thing. I love the
grand arcs and the spirals that the prime numbers seem to describe. They
remind me of exponential power series. Just another example of the
tantalizing bit of order underlying the chaos of the prime numbers:
